Woodstock, Vt.’s Keegan Bradley is not in the running to become golf’s top-ranked player this week but he’ll be looking for his first win since 2012 at the Players Championship.

PONTE VEDRA BEACH, Fla. — As much time as Adam Scott spends away from the PGA Tour, this might have been a good week to take off.

By the mathematical wonder of the world ranking, Scott could have stayed in The Bahamas this week and still moved to No. 1 in the world ranking provided three other players had an ordinary week at The Players Championship.

“See you later,” Scott said with a laugh when told of the scenario.

Scott would love to get to No. 1 for the first time in his career, though he’s more interested in winning big tournaments. Besides, he had a chance at Bay Hill and the Masters to replace Tiger Woods atop the ranking and squandered both chances.

What adds to the interest on the TPC Sawgrass is Scott has company. Henrik Stenson, Masters champion Bubba Watson and Matt Kuchar each have a mathematical chance to reach No. 1 for the first time.

“I don’t think I knew that,” Kuchar said. “That title is a pretty impressive title. To be No. 1 in the world at anything is amazing. To have a chance to be No. 1 in the world in the game of golf, I think all of us that play have those dreams.”

It’s been made possible in part by Woods being on the sidelines. The Players Championship, which starts Thursday, is the second title he is unable to defend this year because of a balky back. Woods had surgery on March 31 and still doesn’t know when he might return.

Woods effectively has owned the No. 1 ranking for the better part of 15 years, his most recent reign dating to his victory last year in the Arnold Palmer Invitational. Other players have reached No. 1 with a caveat. Woods was going through a swing change in 2004 (though Singh helped his cause by winning nine times and a major), and he was going through another swing change and a divorce when he lost the No. 1 ranking from October 2010 to March 2013.

And now he’s not even playing.

But the landscape is changing in golf. Woods has gone six years without a major and is hampered by injuries to his legs, arm and back in recent years. Stenson a year ago became the first player to win the FedEx Cup and Race to Dubai in the same season. Scott won the Masters and became a force in the majors.

“This guy has had as much of a `No. 1’ period as anyone,” Geoff Ogilvy said as he walked onto the short-game area to see Scott stick 24 tees into the ground around the cup for a putting drill. “He contends every time he tees it up. He only plays the big tournaments. After two rounds, it feels like he has a chance in every tournament.”

That sounds a little like Woods, minus the outrageous number of victories.

Even so, Ogilvy remembers the time when someone else got to No. 1 — whether it was Singh in 2004 or Lee Westwood in 2010 — and the murmurs were that Woods was busy changing his swing. Now?

“He seems to be playing better every week than Tiger,” Ogilvy said of Scott. “Tiger won five times last year, but you go to the majors, Scotty seems to be in contention with a chance to win more often than Tiger. If Tiger is your benchmark, he (Scott) has been a better player. Right now, whoever gets to No. 1 probably is. If Henrik wins a major and gets to No. 1, there can’t be an argument.”

Woods still has the nod over two years, the duration of how the ranking measures performances.

In the 26 tournaments that Woods and Scott have played, Woods has won five times (Scott has won twice) and has a 12-11-3 edge in how they finished. However, Scott has a 5-1-1 advantage in the seven majors they have played, winning one of them.

Stenson and Woods have played in 22 tournaments, with Woods having an 11-10-1 advantage (along with four wins to two for Stenson).

Here’s the very least the four contenders have to do for a chance at No. 1:

— Scott has to finish in the top 16.

— Stenson has to finish in the top six.

— Watson has to finish second alone.

— Kuchar has to win.

“It would be the same as the green jacket,” Watson said, describing it as the “pinnacle of the game.”

Scott has the most experience answering the questions, since it has been a mathematical possibility for more than two months. He couldn’t hold a seven-shot lead at Bay Hill going into the weekend with a shot at No. 1. By now, as it was then, he cares more about winning.

“Look, I’m here to win golf tournaments,” Scott said. “That’s been the goal and from that you can get to No. 1 in the world if you win often enough.”